There is no language safer than C in a Unix-like environment, because their shortcomings are well understood by anyone who has taken the time to learn about them.

Saying that C isn't secure because of buffer overflows is a bit silly nowadays.

Memory corruption attacks are going the way of the dodo. The few still working, rely on lazy implementations of exploit prevention technologies or evil designs such as self-modifying-code and custom memory management. All high level management decisions which can be fixed, or not far away from C level.

Most security bugs being talked about in OpenBSD misc@ and tech@ lists nowadays are logic bugs. Most actual exploits for other systems in the wild, exploit logic bugs.

Your hash function drops every other bit because of some logic error and anyone can login as root in about ten attempts? Your web server code uploads any file to a user-specified path, and has permissions for everything? A race condition in your file locks?
No problem, just use Haskell. Oh, wait...

Please tell me how your safe languages will help me.

About proofs, Donald Knuth had this to say.

"Beware of bugs in the above code; I have only proved it correct, not tried it."

It's easy to make something work as designed. It's harder to design something right, especially if you think you don't need to worry about security.